论文标题
解决规范不变子空间的重建量化问题的解决方案
Solution of the Reconstruction-of-the-Measure Problem for Canonical Invariant Subspaces
论文作者
论文摘要
我们研究了对2个可变的加权转移$ w _ {（（α，β）} $的通勤重建问题（ROMP），当给出初始数据作为$ w _ {（α，β）} $的限制的berger量度时，将其与规范的不变量的限制一起，并与MARGARIAME SUBSPACE的量表一起使用，并构成了0-- 0-库的量表。 $ w _ {（α，β）} $。我们证明自然的必要条件确实足够了。当初始数据与可溶性问题相对应时，我们给出了$ w _ {（α，β）} $的Berger度量的具体公式。我们的策略是基于后步扩展和一步扩展的先前结果。一个关键的新定理允许我们解决两步扩展的效果。反过来，这导致了$ \ ell^2（\ Mathbb {z} _+^2）$的任意规范不变子空间的解决方案。
We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts $W_{(α,β)}$, when the initial data are given as the Berger measure of the restriction of $W_{(α,β)}$ to a canonical invariant subspace, together with the marginal measures for the 0-th row and 0-th column in the weight diagram for $W_{(α,β)}$. We prove that the natural necessary conditions are indeed sufficient. When the initial data correspond to a soluble problem, we give a concrete formula for the Berger measure of $W_{(α,β)}$. Our strategy is to build on previous results for back-step extensions and one-step extensions. A key new theorem allows us to solve ROMP for two-step extensions. This, in turn, leads to a solution of ROMP for arbitrary canonical invariant subspaces of $\ell^2(\mathbb{Z}_+^2)$.
